We investigate the extensional ordering of the sequential functionals of finite types, with a focus on when the sequential functionals of a given type form a directed complete partial ordering, andâ€¦ (More)

We prove that if a closed subset X of the Baire space is searchable in the sense of EscardÃ³ [2], and by a functional definable in GÃ¶delâ€™s T, then X is countable, and the Cantor-Bendixson rank of X isâ€¦ (More)

We prove that the sequential functionals of some fixed types at type level 2, taking finite sequences of unary functions as arguments, form a directed complete partial ordering. This gives a fullâ€¦ (More)